This paper presents a numerical method able to isolate all configurations that an arbitrary loop linkage can adopt, within given ranges for its degrees of freedom. The procedure is general, in the sense that it can be applied to single or multiple intermingled loops of arbitrary topology, and complete, in the sense that all possible solutions get accurately bounded, irrespectively of whether the analyzed linkage is rigid or mobile. The problem is tackled by formulating a system of linear, parabolic, and hyperbolic equations, which is here solved by a new strategy exploiting its structure. The method is conceptually simple, geometric in nature, and easy to implement, yet it provides solutions at the desired accuracy in short computation times.

This work was supported by the project 'Planificador de trayectorias para sistemas robotizados de arquitectura arbitraria' (J-00930).

Robotics: Science and Systems Conference (RSS), 2006, Filadelfia (EE.UU.)

Peer Reviewed